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Question: Use the Racetrack Principle to show that ln x ≤ x - 1.
Use the fact that ln x and ex are inverse functions to show that the inequalities ex ≥ 1+x and ln x ≤ x-1 are equivalent for x > 0.
How many minutes, to the nearest tenth, does it take the submarine to reach a depth of 180 feet? Be sure to include a sketch.
What is the probability that Mr. Smith has two sons?" Show that there are two different answers to this puzzle, depending on whether Mr. Smith specifi- cally mentioned his son because he was born on a Tuesday or whether he randomly chose a child a..
Estimate the area under the graph of f(x)= (x^2) + x from x=0 to x=3 using 3 approximating rectangles and left endpoints.
If the box is to have a volume of 72 cubic inches, find the length and width of the cardboard that must be used.
Suppose that Al, Betty and Karl are dividing a half- cheese and half- pepperoni pizza. They use the lone shoose method. Betty is the chhoser and Karl and Al are thedividers.
Represent the function f(t) as a summation of an even and an odd signal. Sketch the even and odd parts.
On a map 1 inch represents 58 miles. The distance between two cities on the same map is 5.85 inches. How many miles apart are the two cities?
Give some properties of a simple graph that imply that it does not have a Hamilton circuit.
What is the nature of the effects of the factors studied in this experiment? What strategy would you use to reduce invoice errors, given the results of this experiment?
According to the value of z(I) obtained before, determine whether the use of the BL heuristic allows one to obtain the minimum number of bins used.
Poisson Kernel and Harmonic Function, Let P_r(t)=R((1+z)/(1-z)), z=re^it be the Poisson kernel for the unit disc |z|
A formula for calculating the distance, d, that can be see from an airplane to the horizon is d=1.22x^1/2, where x is the altitude of the plane in feet and d is given in miles. How far can one see to the horizon in a plane flying at 12,734 feet? R..
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